Question

LAB 2 APROXIMATING ZEROS OF FUNCTIONS USING NEWTON'S METHOD (Refer to section 3.8 of your textbook for details in the derivation of the method and sample problems) (NOTE: You can use Derive, MicrosoftMathematics or Mathematica or any other Computer Algebra System of your choice. Your final report must be clear and concise. You must also provide sufficient comments on your approach and the final results in a manner that will make your report clear and accessible to anyone who is familiar with the basic concepts, operations and applications of calculusI.) Summary of Newton's Method: Given a function f(x) and its derivative f '(x), we begin with a first guess ro for a root of the function. Provided the function is reasonably well-behaved a better approximation x1 is f(xo) - 0x= I Geometrically, X1 is the intersection with the x-axis of a line tangent to f at f(xo). The process is repeated until a sufficiently accurate value is reached: Xn+1 n ( (The following links provide interesting graphical and analytical presentations). https://en.wikipedia.org/wiki/Newton%27s_method Exercise 1 Use Newton's method to find the real root of f(x) = x3-x - 1, accurate to four decimal places. You can use xo= 1. Exercise 2 Can you use Newton's method in an attempt to find a real root of f(x) =x -2x - 2, with xo = 0 ? (Explain your answer)

Answer 1

I

2-22-2 fCu) -) 32 3-1 3478 3 325 23 u 32 4t A5 32 47